/*
Generators and relations for A_4 from Ex 7.13. The exercise
is to prove that the finitely presented group
G233 = < x,y | x^2, y^3, (x*y)^3 > is A4. The method is
to list the elements, and to show that multiplying by the
generators takes us back into the list, using only the
stated relations.
*/

A4 := Alt(4);
x := A4!((1,2)(3,4)); y := A4!(1,2,3); x*y;
L := [Id(A4), x, y, y^2, x*y, x*y^2, y*x, y^2*x, x*y*x,
   x*y^2*x, y*x*y^2, x*y*x*y^2]; #L; #SequenceToSet(L);